Abstract

We present a new method for measuring the group dispersion of the fundamental mode of a holey fiber over a wide wavelength range by white-light interferometry employing a low-resolution spectrometer. The method utilizes an unbalanced Mach-Zehnder interferometer with a fiber under test placed in one arm and the other arm with adjustable path length. A series of spectral signals are recorded to measure the equalization wavelength as a function of the path length, or equivalently the group dispersion. We reveal that some of the spectral signals are due to the fundamental mode supported by the fiber and some are due to light guided by the outer cladding of the fiber. Knowing the group dispersion of the cladding made of pure silica, we measure the wavelength dependence of the group effective index of the fundamental mode of the holey fiber. Furthermore, using a full-vector finite element method, we model the group dispersion and demonstrate good agreement between experiment and theory.

© 2007 Optical Society of America

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  1. L.G. Cohen, "Comparison of single-mode fiber dispersion measurement techniques," J. Lightwave Technol. 3, 958-966 (1985).
    [CrossRef]
  2. S. Diddams and J.C. Diels, "Dispersion measurements with white-light interferometry," J. Opt. Soc. Am. B 13, 1120-1128 (1995).
    [CrossRef]
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    [CrossRef]
  4. M.J. Saunders and W.B. Gardner, "Interferometric determination of dispersion variations in single-mode fibers," J. Lightwave Technol. 5, 1701-1705 (1987).
    [CrossRef]
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    [CrossRef]
  6. P. Lu, H. Ding, and S.J. Mihailov, "Direct measurement of the zero-dispersion wavelength of tapered fibres using broadband-light interferometry," Meas. Sci. Technol. 16, 1631-1636 (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. P. Hlubina, "White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica," Opt. Commun. 193, 1-7 (2001).
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    [CrossRef]
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    [CrossRef]
  17. P. Hlubina, M. Szpulak, L. Knyblová, G. Statkiewicz, T. Martynkien, D. Ciprian, and W. Urbanczyk, "Measurement and modelling of dispersion characteristics of two-mode birefringent holey fibre," Meas. Sci. Technol. 17, 626-630 (2006).
    [CrossRef]
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2007 (1)

P. Hlubina, R. Chlebus, and D. Ciprian, "Differential group refractive index dispersion of glasses of optical fibres measured by a white-light spectral interferometric technique," Meas. Sci. Technol. 18, 1547-1552 (2007).
[CrossRef]

2006 (3)

L. Labonté, P. Roy, F. Pagnoux, F. Louradour, C. Restoin, G. Mélin, and E. Burov, "Experimental and numerical analysis of the chromatic dispersion dependence upon the actual profile of small core microstructured fibres," J. Opt. A: Pure App. Opt. 8, 933-938 (2006).
[CrossRef]

P. Hlubina, M. Szpulak, L. Knyblová, G. Statkiewicz, T. Martynkien, D. Ciprian, and W. Urbanczyk, "Measurement and modelling of dispersion characteristics of two-mode birefringent holey fibre," Meas. Sci. Technol. 17, 626-630 (2006).
[CrossRef]

J.Y. Lee and D.Y. Kim, "Versatile chromatic dispersion measurement of a single mode fiber using spectral white light interferometry," Opt. Express 14, 11608-11614 (2006).
[CrossRef] [PubMed]

2005 (1)

P. Lu, H. Ding, and S.J. Mihailov, "Direct measurement of the zero-dispersion wavelength of tapered fibres using broadband-light interferometry," Meas. Sci. Technol. 16, 1631-1636 (2005).
[CrossRef]

2004 (1)

2003 (3)

2002 (1)

2001 (3)

P. Hlubina, "White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica," Opt. Commun. 193, 1-7 (2001).
[CrossRef]

F. Koch, S.V. Chernikov, and J.R. Taylor, "Dispersion measurement in optical fibres over the entire spectral range from 1.1 μmm to 1.7 μmm," Opt. Commun. 175, 209-213 (2001).
[CrossRef]

D. Ouzounov, D. Homoelle, W. Zipfel, W.W. Webb, A.L. Gaeta, J.A. West, J.C. Fajardo, and K.W. Koch, "Dispersion measurements of microstructure fibers using femtosecond laser pulses," Opt. Commun. 192, 219-223 (2001).
[CrossRef]

1995 (1)

1994 (1)

M. Koshiba, S. Maruyama, and K. Hirayama, "A vector finite element method with the higher order mixed-interpolation-type triangular elements for optical waveguide problems," J. Lightwave Technol. 12, 495-502 (1994).
[CrossRef]

1989 (1)

P. Merritt, R.P. Tatam, and D.A. Jackson, "Interferometric chromatic dispersion measurements on short lengths of monomode optical fiber," J. Lightwave Technol. 7, 703-716 (1989).
[CrossRef]

1987 (1)

M.J. Saunders and W.B. Gardner, "Interferometric determination of dispersion variations in single-mode fibers," J. Lightwave Technol. 5, 1701-1705 (1987).
[CrossRef]

1985 (1)

L.G. Cohen, "Comparison of single-mode fiber dispersion measurement techniques," J. Lightwave Technol. 3, 958-966 (1985).
[CrossRef]

1981 (1)

M. Tateda, N. Shibata, and S. Seikai, "Interferometric method for chromatic dispersion measurement in a singlemode optical fiber," IEEE J. Quantum Electron. 17, 404-407 (1981).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

M. Tateda, N. Shibata, and S. Seikai, "Interferometric method for chromatic dispersion measurement in a singlemode optical fiber," IEEE J. Quantum Electron. 17, 404-407 (1981).
[CrossRef]

J. Lightwave Technol. (4)

M.J. Saunders and W.B. Gardner, "Interferometric determination of dispersion variations in single-mode fibers," J. Lightwave Technol. 5, 1701-1705 (1987).
[CrossRef]

P. Merritt, R.P. Tatam, and D.A. Jackson, "Interferometric chromatic dispersion measurements on short lengths of monomode optical fiber," J. Lightwave Technol. 7, 703-716 (1989).
[CrossRef]

L.G. Cohen, "Comparison of single-mode fiber dispersion measurement techniques," J. Lightwave Technol. 3, 958-966 (1985).
[CrossRef]

M. Koshiba, S. Maruyama, and K. Hirayama, "A vector finite element method with the higher order mixed-interpolation-type triangular elements for optical waveguide problems," J. Lightwave Technol. 12, 495-502 (1994).
[CrossRef]

J. Opt. A: Pure App. Opt. (1)

L. Labonté, P. Roy, F. Pagnoux, F. Louradour, C. Restoin, G. Mélin, and E. Burov, "Experimental and numerical analysis of the chromatic dispersion dependence upon the actual profile of small core microstructured fibres," J. Opt. A: Pure App. Opt. 8, 933-938 (2006).
[CrossRef]

J. Opt. Soc. Am. B (1)

Meas. Sci. Technol. (3)

P. Hlubina, R. Chlebus, and D. Ciprian, "Differential group refractive index dispersion of glasses of optical fibres measured by a white-light spectral interferometric technique," Meas. Sci. Technol. 18, 1547-1552 (2007).
[CrossRef]

P. Hlubina, M. Szpulak, L. Knyblová, G. Statkiewicz, T. Martynkien, D. Ciprian, and W. Urbanczyk, "Measurement and modelling of dispersion characteristics of two-mode birefringent holey fibre," Meas. Sci. Technol. 17, 626-630 (2006).
[CrossRef]

P. Lu, H. Ding, and S.J. Mihailov, "Direct measurement of the zero-dispersion wavelength of tapered fibres using broadband-light interferometry," Meas. Sci. Technol. 16, 1631-1636 (2005).
[CrossRef]

Opt. Commun. (3)

P. Hlubina, "White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica," Opt. Commun. 193, 1-7 (2001).
[CrossRef]

F. Koch, S.V. Chernikov, and J.R. Taylor, "Dispersion measurement in optical fibres over the entire spectral range from 1.1 μmm to 1.7 μmm," Opt. Commun. 175, 209-213 (2001).
[CrossRef]

D. Ouzounov, D. Homoelle, W. Zipfel, W.W. Webb, A.L. Gaeta, J.A. West, J.C. Fajardo, and K.W. Koch, "Dispersion measurements of microstructure fibers using femtosecond laser pulses," Opt. Commun. 192, 219-223 (2001).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Proc. SPIE (1)

P. Hlubina and I. Gurov, "Spectral interferograms including the equalization wavelengths processed by autoconvolution method," Proc. SPIE 5064, 198-205 (2003).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup with an unbalanced Mach-Zehnder interferometer to measure the group dispersion of the mode supported by a fiber under test.

Fig. 2.
Fig. 2.

(a) SEM photograph of the investigated holey fiber and (b) binary mask used for mesh generation.

Fig. 3.
Fig. 3.

Calculated phase (a) and group (b) effective indices of the LP01 mode of respective polarizations as a function of wavelength.

Fig. 4.
Fig. 4.

Examples of the recorded spectral signals: (a) optical components (OCs), fiber plus optical components (F+OCs); (b) optical components (OCs), glass plus optical components (G+OCs).

Fig. 5.
Fig. 5.

Path length difference (a) and group effective index (b) measured as a function of wavelength: optical components (OCs), fiber plus optical components (F+OCs), glass plus optical components (G+OCs); LP01 mode, pure silica (solid lines are theoretical functions).

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

Δ MZ g ( λ ) = L l N eff ( λ ) z N c ( λ ) d ,
N ( λ ) = n ( λ ) λ d n ( λ ) d λ .
L o ( λ 0 ) = N eff ( λ 0 ) z + N c ( λ 0 ) d + l .
L g ( λ 0 ) = N g ( λ 0 ) z + N c ( λ 0 ) d + l ,
N eff ( λ 0 ) = N g ( λ 0 ) + [ L o ( λ 0 ) L g ( λ 0 ) ] z ,
Δ L c ( λ 0 ) = Δ N c ( λ 0 ) d ,
L g ( λ 0 ) = L g ( λ 0 r ) + Δ N g ( λ 0 ) z + Δ N c ( λ 0 ) d ,
N eff ( λ 0 ) = N g ( λ 0 r ) + [ L o ( λ 0 ) L g ( λ 0 r ) Δ L c ( λ 0 ) ] z ,
[ × × + k 0 2 ε ( r ) 0 0 0 ] [ E E z ] = β 2 [ 1 Δ + k 0 2 ε ( r ) ] [ E E z ] ,
δ ( N eff ) = [ d N g ( λ 0 r ) d λ 0 r δ ( λ 0 r ) ] 2 + [ δ ( Δ L ) z ] 2 + [ Δ L δ ( z ) z 2 ] 2 .

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